Department of

# Mathematics

Seminar Calendar
for Special Topology, Group Theory, and Number Theory Seminar events the year of Wednesday, September 9, 2009.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, September 2, 2009

3:00 pm in 345 Altgeld Hall,Wednesday, September 2, 2009

#### Congruence subgroups of mapping class groups (especially braid groups.)

###### Jordan Ellenberg (University of Wisconsin, Madison)

Abstract: Abstract: There is a notion of "congruence subgroup" of a mapping class group which appears to have certain properties in common with congruence subgroups of arithmetic groups. We will discuss several open problems in the theory of congruence subgroups, some progress, and applications: for instance, the proof of a "strong congruence subgroup property" for the mapping class group of a once-punctured elliptic curve answers an open question from dynamics about Teichmuller curves in moduli spaces of curves (joint work with D.B. McReynolds). In number theory, theorems about stabilization of cohomology of congruence subgroups yield results towards the Cohen-Lenstra heuristics for ideal class groups over function fields over finite fields. (joint work with A. Venkatesh, C. Westerland.)